Brownian Motors and Stochastic Resonance

TL;DR

This paper investigates how noise-induced stochastic resonance enhances transport in a coupled particle system on a ratchet potential, revealing an optimal noise level for maximum response and velocity.

Contribution

It introduces a model of a two-particle coupled system on a ratchet, demonstrating the link between stochastic resonance and directed transport.

Findings

Maximum system response occurs at an optimal noise level.

Average velocity peaks at the same noise level as the response.

Stochastic resonance significantly enhances ratchet-driven transport.

Abstract

We study the transport properties for a walker on a ratchet potential. The walker consists of two particles coupled by a bistable potential that allow the interchange of the order of the particles while moving through a one-dimensional asymmetric periodic ratchet potential. We consider the stochastic dynamics of the walker on a ratchet with an external periodic forcing, in the overdamped case. The coupling of the two particles corresponds to a single effective particle, describing the internal degree of freedom, in a bistable potential. This double-well potential is subjected to both a periodic forcing and noise, and therefore is able to provide a realization of the phenomenon of stochastic resonance. The main result is that there is an optimal amount of noise where the amplitude of the periodic response of the system is maximum, a signal of stochastic resonance, and that precisely for this optimal noise the average velocity of the walker is maximal, implying a strong link between stochastic resonance and the ratchet effect.